Transformation Interactive Notes - Ms. Olsen's Weebly

[Pages:9]Transformations Interactive Notes

Translations, Dilations, Rotations and Reflections

This product involves four pages of interactive notes on translations, dilations, rotations and reflections. Each note page provides an opportunity for students to complete the definition, examine and compare the angles and sides of the images, list the pre-image and image coordinates and to describe in words the transformation completed. A graph is provided with the pre-image. Students can use colored pencils to graph the additional images.

An answer key is provided.

Complete the notes on transformations. Cut out the notes along the dotted lines and glue them in your notebook.

Translations

A transformation in which each point of a figure moves

the same

in the same

.

In a translation, the pre-image & image are

.

The corresponding angles have the The corresponding sides have the

measurement. measurement.

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create two new translated images.

Pre-Image A ( , ) B ( , ) C ( , )

Image (x + 5, y + 2) A ( , ) B ( , ) C ( , ) In words, describe the translation.

Image (x + 8, y - 8) A ( , ) B ( , ) C ( , ) In words, describe the translation.

A BC

Using two different colored pencils, graph the new images. Make sure to label both figures.

What rule could be used to translate the figure so it would be located in quadrant 3?

(

,

)

Translations

A transformation in which each point of a figure moves

the same

in the same

.

In a translation, the pre-image & image are

.

The corresponding angles have the The corresponding sides have the

measurement. measurement.

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create two new translated images.

Pre-Image A ( , ) B ( , ) C ( , )

Image (x + 5, y + 2) A ( , ) B ( , ) C ( , ) In words, describe the translation.

Image (x + 8, y - 8) A ( , ) B ( , ) C ( , ) In words, describe the translation.

A BC

Using two different colored pencils, graph the new images. Make sure to label both figures.

What rule could be used to translate the figure so it would be located in quadrant 3?

(

,

)

? The Clever Clover, 2016

Dilations

A transformation in which each point of a figure

or

with respect to a fixed point,

called the

.

In a translation, the pre-image & image are

.

The corresponding angles have the

measurement.

The corresponding sides are

.

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create two new translated images.

Pre-Image A ( , ) B ( , ) C ( , )

Image (2x, 2y)

A ( , ) B ( , ) C ( , )

In words, describe the dilation.

Image (!x, !y)

""

A ( , ) B ( , ) C ( , )

In words, describe the dilation.

A BC

Using two different colored pencils, graph the new images. Make sure to label both figures.

Compare the area of the pre-image to the image. Did the area double in size?

Dilations

A transformation in which each point of a figure

or

with respect to a fixed point,

called the

.

In a translation, the pre-image & image are

.

The corresponding angles have the

measurement.

The corresponding sides are

.

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create two new translated images.

Pre-Image A ( , ) B ( , ) C ( , )

Image (2x, 2y)

A ( , ) B ( , ) C ( , )

In words, describe the dilation.

Image (!x, !y)

""

A ( , ) B ( , ) C ( , )

In words, describe the dilation.

A BC

Using two different colored pencils, graph the new images. Make sure to label both figures.

Compare the area of the pre-image to the image. Did the area double in size?

? The Clever Clover, 2016

Complete the notes on transformations. Cut out the notes along the dotted lines and glue them in your notebook.

Rotations

A transformation in which a figure is a given angle, called the direction about a fixed point, called the

through , and in a given

.

In a rotation, the pre-image & image are

.

The corresponding angles have the

measurement.

The corresponding sides have the

measurement.

90? Clockwise 90? Counter Clockwise 180? Rotation

(x, y) f (y, -x)

(x, y) f (-y, x)

(x, y) f (-x, -y)

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create three new rotated images.

Pre-Image Coordinates A ( , )

B( , )

C( , )

90? Clockwise

A ( , ) B ( , ) C ( , )

90? Counter

Clockwise

A ( , ) B ( , ) C ( , )

180? Rotation

A ( , ) B ( , ) C ( , )

Using three different

A

colored pencils, graph the new images. Make sure to

label all of the figures.

BC

What would the coordinates be if the pre-image was rotated 270? clockwise?

Rotations

A transformation in which a figure is a given angle, called the direction about a fixed point, called the

through , and in a given

.

In a rotation, the pre-image & image are

.

The corresponding angles have the

measurement.

The corresponding sides have the

measurement.

90? Clockwise 90? Counter Clockwise 180? Rotation

(x, y) f (y, -x)

(x, y) f (-y, x)

(x, y) f (-x, -y)

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create three new rotated images.

Pre-Image Coordinates A ( , )

B( , )

C( , )

90? Clockwise

A ( , ) B ( , ) C ( , )

90? Counter

Clockwise

A ( , ) B ( , ) C ( , )

180? Rotation

A ( , ) B ( , ) C ( , )

Using three different

A

colored pencils, graph the new images. Make sure to

label all of the figures.

BC

What would the coordinates be if the pre-image was rotated 270? clockwise?

? The Clever Clover, 2016

Complete the notes on transformations. Cut out the notes along the dotted lines and glue them in your notebook.

Reflections

A transformation in which a figure is

,

in a line, called the

.

In a rotation, the pre-image & image are

.

The corresponding angles have the

measurement.

The corresponding sides have the

measurement.

Reflection in the x - axis

Reflection in the y-axis

(x, y) f (x, -y)

(x, y) f (-x, y)

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create three new rotated images.

Pre-Image Coordinates A ( , )

B( , )

C( , )

Reflection in the x-axis A ( , )

B ( , )

C ( , )

Reflection in the y-axis A ( , ) B ( , ) C ( , )

Reflections

A transformation in which a figure is

,

in a line, called the

.

In a reflection, the pre-image & image are

.

The corresponding angles have the

measurement.

The corresponding sides have the

measurement.

Reflection in the x - axis

Reflection in the y-axis

(x, y) f (x, -y)

(x, y) f (-x, y)

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create three new rotated images.

Pre-Image Coordinates A ( , )

B( , )

C( , )

Reflection in the x-axis A ( , ) B ( , ) C ( , )

Reflection in the y-axis A ( , ) B ( , ) C ( , )

A BC

Using two different colored pencils, graph the new images. Make sure to label all of the figures.

A figure has line

symmetry if a line, called

the

,

divides the figure into two

parts that are

of each

other in the line.

A BC

Using two different colored pencils, graph the new images. Make sure to label all of the figures.

A figure has line

symmetry if a line, called

the

,

divides the figure into two

parts that are

of each

other in the line.

? The Clever Clover, 2016

Complete the notes on transformations. Cut out the notes along the dotted lines and glue them in your notebook.

Translations

A transformation in which each point of a figure moves the same distance in the same direction.

In a translation, the pre-image & image are congruent.

The corresponding angles have the same measurement. The corresponding sides have the same measurement.

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create two new translated images.

Pre-Image A (-8 , 8)

B (-8 , 3)

C (-4 , 3)

Image (x + 5, y + 2) A (-3 , 10)

B (-3 , 5)

C ( 1 , 5)

In words, describe the translation. The image moved five units to the right and up two units.

Image (x + 8, y - 8) A (0 , 0)

B (0 , -5)

C (4, -5)

In words, describe the translation. The image movedeight units to the right and down eight units.

A A

B

C

BC

A

B

C

Using two different colored pencils, graph the new images. Make sure to label both figures.

What rule could be used to translate the figure so it would be located in quadrant 3?

Possible Answer: (x - 1 , y - 10)

Dilations

A transformation in which each point of a figure stretches or shrinks with respect to a fixed point, called the center of dilation. In a translation, the pre-image & image are similar. The corresponding angles have the same measurement. The corresponding sides are proportional.

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create two new translated images.

Pre-Image A (0, 5)

B (0 , 0)

C (5, 0)

Image (2x, 2y)

A (0, 10)

B (0, 0)

C (10 , 0)

In words, describe the dilation. The image doubled in size.

Image (!x, !y)

""

A (0 , 2.5) B (0 , 0)

C (2.5, 0)

In words, describe the dilation. The image is half the size of the pre-image.

A

A A

Using two different colored pencils, graph the new images. Make sure to label both figures.

BB C" C B

C Compare the area of the pre-image to the image. Did the area double in size?

? The Clever Clover, 2016

Complete the notes on transformations. Cut out the notes along the dotted lines and glue them in your notebook.

Rotations

A transformation in which a figure is turned

through

a given angle, called the angle of rotation, and in a given

direction about a fixed point, called the center of rotation.

In a rotation, the pre-image & image are congruent. The corresponding angles have the same measurement. The corresponding sides have the same measurement.

90? Clockwise 90? Counter Clockwise 180? Rotation

(x, y) f (y, -x)

(x, y) f (-y, x)

(x, y) f (-x, -y)

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create three new rotated images.

Pre-Image Coordinates A (2, 6)

B (2, 1 )

C (6, 1 )

90? Clockwise

A (6 , -2)

B (1 , -2)

C (1, -6)

90? Counter Clockwise

180? Rotation

A (-6, 2) A (-2 , -6)

B (-1, 2) B (-2, -1)

C (-1, 6) C (-6, -1)

C A A

B B C C B B A

A C

Using three different colored pencils, graph the new images. Make sure to label all of the figures.

What would the coordinates be if the pre-image was rotated 270?? The coordinates would be the same as the 90? counter clockwise coordinates.

Reflections

A transformation in which a figure is reflected or flipped in a line, called the line of reflection.

In a reflection, the pre-image & image are congruent. The corresponding angles have the same measurement. The corresponding sides have the same measurement.

Reflection in the x - axis

Reflection in the y-axis

(x, y) f (x, -y)

(x, y) f (-x, y)

Look at the graph below. Record the coordinate pairs for the pre-image. Using the pre-image points, create three new rotated images.

Pre-Image Coordinates A (3, 8)

B (3, 3)

C (7, 3)

Reflection in the x-axis A (3, -8)

B (3, -3)

C (7, -3)

Reflection in the y-axis A (-3, 8)

B (-3, 3)

C (-7, 3)

A A C B B C

B C A

Using two different colored pencils, graph the new images. Make sure to label all of the figures.

A figure has line symmetry if a line, called the line of symmetry, divides the figure into two parts that are reflections of each other in the line.

? The Clever Clover, 2016

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